Coincidentally, I came across a video today which describe in laymen terms what time crystals are: https://www.youtube.com/watch?v=ieDIpgso4no

tl;dw: Crystals are materials which atoms or molecules are aranged in a repeating manner. Time crystals are a material which isn't just repeating in the three dimensions of space but also in the "time dimension". Basically, the quantum spin of the material switches regularly, even though no energy is being applied.